Abstract:The circuitry of cortical networks involves interacting
populations of excitatory (E) and inhibitory (I) neurons whose relationships are now known to a large extent. Inputs to
E-cells and I-cells may have their origins in remote or local
cortical areas. We consider a rudimentary
model involving E- and I-cells.
One of our goals is to test an analytic approach to finding firing
rates in neural networks without using a diffusion approximation and to this end
we consider in detail networks of excitatory neurons with leaky integrate-and-fire (LIF)
dynamics. A simple measure of synchronization, denoted by , where q
is between 0 and 100 is introduced. Fully connected
E-networks have a large tendency to
become dominated by synchronously firing
groups of cells, except when inputs are relatively weak.
We observed random or asynchronous firing in such networks with
diverse sets of parameter values. When such firing patterns were found,
the analytical approach was often able to accurately predict average neuronal firing rates.
We also considered several properties of E-E networks, distinguishing
several kinds of firing pattern. Included were
those with silences before or after periods of intense activity or with periodic synchronization.
We investigated the occurrence of synchronized firing with respect to
changes in the internal excitatory postsynaptic
potential (EPSP) magnitude in a network of 100 neurons with fixed values of the
remaining parameters.
When the internal EPSP size was less than a certain value, synchronization was absent.
The amount of synchronization then
increased slowly as the EPSP amplitude increased until at a particular
EPSP size the amount of synchronization abruptly increased, with attaining
the maximum value of 100%.
We also found network frequency transfer characteristics for various
network sizes and found a linear dependence of firing frequency over wide
ranges of the external afferent frequency, with nonlinear effects at lower input mnfrequencies. The theory may also be applied to sparsely connected networks whose firing behaviour was found to change abruptly as the
probability of a connection passed through a critical value.
The analytical method was also
found to be useful for a feed-forward excitatory network and a network
of excitatory and inhibitory neurons.